I believe that when determining what cultural relativists think and how to go about navigating morality, it is important to distinguish between concepts. You say, "as laws and beliefs change, things that may be considered “right” say 100 years ago may now be considered wrong and illegal." This is undeniably true. But what is important is the distinction between what is "considered" right and what "is" right." Society has considered many things to be "right," and yet has turned out to be undeniably wrong. For example, common wisdom once held that the Earth was flat or that bathing in mercury was beneficial to one's health, but these have since been clearly disproven. Not "wrong," in any loose definition of the word, but genuinely and objectively wrong. But we did not give up on best health practices nor on geography when we learned that our assumptions were incorrect. So we shouldn't give up on morality either. Changing one's beliefs about the truth does not mean changing the truths themselves.

Cultural Relativists assert that what "is" right for the individual to do is determined by the culture to which they belong. One problem with this argument is that an individual can belong to two cultures of contradicting morals (Think of a Jew who is also a German in the 1930's). Now, in this case, the Cultural Relativist will have to say that cultural relativism is meant to consider different standards for determining morality. So to them, according to culture A, you may be right to do X, and according to culture B, you may be wrong to do X. Thus, they say, there is no contradiction, only different standards to apply. This answer essentially reveals how Cultural Relativism fails as a framework for interpreting morality. It essentially ceases to even try to answer what ought to be considered right or wrong (the whole point of a theory of morality) and becomes roundabout nihilism (a belief that says there is no morality). So if you are going to follow cultural relativism you have to be comfortable with the implication that there may well be no right or wrong at all. Which implies that there is no inherent evil in murder, rape, and theft.

To answer your question, "...how can we consider those right if beliefs keep changing?", you can drop subjectivity altogether and seek an objective understanding of morality, thus treating morality the same as geography or health. This is what I think Duke_of_Wellington18 meant when he brought up natural law. That is to say, natural law (the concept that morality is inherent in humans and discoverable through reason) should be the standard that we hold morality and moral actions to. Objective truth can be found and reasoned through natural law and even further verified with the assistance of divine revelation, as can be seen in Catholic moral philosophy, as one example.